Use the \lecture command for each one of your lectures (refer to the
beamer manual, Section 10.4 Splitting a Course Into Lectures), and then add
\renewcommand\thetheorem{\arabic{lecture}.\arabic{theorem}}
\makeatletter
\@addtoreset{theorem}{lecture}
\makeatother
to the preamble of your document. This will produce the desired result for theorems and the other predefined theorem-like structures; for newly user-defined structures (such as remark in your example), you'll need a similar set of commands:
\renewcommand\theremark{\arabic{lecture}.\arabic{remark}}
\makeatletter
\@addtoreset{remark}{lecture}
\makeatother
A complete example:
\documentclass[]{beamer}
\usetheme{CambridgeUS}
\setbeamertemplate{theorems}[numbered]
\newtheorem{remark}{Remark} %for remark
\renewcommand\thetheorem{\arabic{lecture}.\arabic{theorem}}
\renewcommand\theremark{\arabic{lecture}.\arabic{remark}}
\makeatletter
\@addtoreset{theorem}{lecture}
\@addtoreset{remark}{lecture}
\makeatother
\begin{document}
\lecture{Test lecture one}{lone}
\section{First section of lecture one}
\begin{frame}
\frametitle{Theorems}
\begin{theorem} This is theorem 1. \end{theorem}
\begin{theorem} This is theorem 2. \end{theorem}
\begin{corollary} This is a test corollary \end{corollary}
\begin{remark} This is a test remark \end{remark}
\end{frame}
\lecture{Test lecture two}{ltwo}
\section{First section of lecture two}
\begin{frame}
\frametitle{Theorems}
\begin{theorem} This is theorem 1. \end{theorem}
\begin{theorem} This is theorem 2. \end{theorem}
\begin{corollary} This is a test corollary \end{corollary}
\begin{remark} This is a test remark \end{remark}
\end{frame}
\end{document}
The result, showing the numbering for the two lectures:
